Speaker: Michael Nivala, Applied Mathematics
Title:
Time: 3:30 PM, Thursday, 4/21/05
Place: Guggenheim Room 408d
Abstract:
Homotopy methods are powerful tools originating in differential geometry and the calculus of variations for the integration of exact expressions. In one spatial dimensions, this amounts to integrating total derivatives of expressions containing unknown functions and their derivatives. Such calculations occur frequently when dealing with soliton equations, for instance when determining the functional form of consecutive conserved densities and their fluxes.
The current version of mathematica fails at even simple examples. Both maple and mathematica refuse to integrate expressions that are sums of derivative and nonderivative terms, even when the vast majority of the terms may be integrated. Combining an optimization approach with the homotopy method we present an algorithm for the integration of expressions that are not total derivatives, but contain many terms that are.
Everyone welcome!